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<h1>Module <code>pl.array2d</code></h1>
<p>Operations on two-dimensional arrays.</p>
<p> See <a href="../manual/02-arrays.md.html#Operations_on_two_dimensional_tables">The Guide</a></p>

<p> The size of the arrays is determined by using the length operator <code>#</code> hence
 the module is not <code>nil</code> safe, and the usual precautions apply.</p>

<p> Note: all functions taking <code>i1,j1,i2,j2</code> as arguments will normalize the
 arguments using <a href="../libraries/pl.array2d.html#default_range">default_range</a>.</p>

<p> Dependencies: <a href="../libraries/pl.utils.html#">pl.utils</a>, <a href="../libraries/pl.tablex.html#">pl.tablex</a>, <a href="../libraries/pl.types.html#">pl.types</a></p>


<h2><a href="#Functions">Functions</a></h2>
<table class="function_list">
	<tr>
	<td class="name" nowrap><a href="#size">size (a)</a></td>
	<td class="summary">return the row and column size.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#column">column (a, j)</a></td>
	<td class="summary">extract a column from the 2D array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#row">row (a, i)</a></td>
	<td class="summary">extract a row from the 2D array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#map">map (f, a, arg)</a></td>
	<td class="summary">map a function over a 2D array</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#reduce_rows">reduce_rows (f, a)</a></td>
	<td class="summary">reduce the rows using a function.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#reduce_cols">reduce_cols (f, a)</a></td>
	<td class="summary">reduce the columns using a function.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#reduce2">reduce2 (opc, opr, a)</a></td>
	<td class="summary">reduce a 2D array into a scalar, using two operations.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#map2">map2 (f, ad, bd, a, b, arg)</a></td>
	<td class="summary">map a function over two arrays.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#product">product (f, t1, t2)</a></td>
	<td class="summary">cartesian product of two 1d arrays.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#flatten">flatten (t)</a></td>
	<td class="summary">flatten a 2D array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#reshape">reshape (t, nrows, co)</a></td>
	<td class="summary">reshape a 2D array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#transpose">transpose (t)</a></td>
	<td class="summary">transpose a 2D array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#swap_rows">swap_rows (t, i1, i2)</a></td>
	<td class="summary">swap two rows of an array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#swap_cols">swap_cols (t, j1, j2)</a></td>
	<td class="summary">swap two columns of an array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#extract_rows">extract_rows (t, ridx)</a></td>
	<td class="summary">extract the specified rows.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#extract_cols">extract_cols (t, cidx)</a></td>
	<td class="summary">extract the specified columns.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#remove_row">remove_row (t, i)</a></td>
	<td class="summary">remove a row from an array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#remove_col">remove_col (t, j)</a></td>
	<td class="summary">remove a column from an array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#parse_range">parse_range (s)</a></td>
	<td class="summary">parse a spreadsheet range.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#range">range (t, rstr)</a></td>
	<td class="summary">get a slice of a 2D array using spreadsheet range notation.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#default_range">default_range (t, i1, j1, i2, j2)</a></td>
	<td class="summary">normalizes coordinates to valid positive entries and defaults.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#slice">slice (t, i1, j1, i2, j2)</a></td>
	<td class="summary">get a slice of a 2D array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#set">set (t, value, i1, j1, i2, j2)</a></td>
	<td class="summary">set a specified range of an array to a value.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#write">write (t, f, fmt, i1, j1, i2, j2)</a></td>
	<td class="summary">write a 2D array to a file.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#forall">forall (t, row_op, end_row_op, i1, j1, i2, j2)</a></td>
	<td class="summary">perform an operation for all values in a 2D array.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#move">move (dest, di, dj, src, i1, j1, i2, j2)</a></td>
	<td class="summary">move a block from the destination to the source.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#iter">iter (a, indices, i1, j1, i2, j2)</a></td>
	<td class="summary">iterate over all elements in a 2D array, with optional indices.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#columns">columns (a)</a></td>
	<td class="summary">iterate over all columns.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#rows">rows (a)</a></td>
	<td class="summary">iterate over all rows.</td>
	</tr>
	<tr>
	<td class="name" nowrap><a href="#new">new (rows, cols, val)</a></td>
	<td class="summary">new array of specified dimensions</td>
	</tr>
</table>

<br/>
<br/>


    <h2 class="section-header "><a name="Functions"></a>Functions</h2>

    <dl class="function">
    <dt>
    <a name = "size"></a>
    <strong>size (a)</strong>
    </dt>
    <dd>
    return the row and column size.
 Size is calculated using the Lua length operator #, so usual precautions
 regarding <code>nil</code> values apply.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         a 2d array
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>
        <li>
           <span class="types"><span class="type">int</span></span>
        number of rows (<code>#a</code>)</li>
        <li>
           <span class="types"><span class="type">int</span></span>
        number of cols (<code>#a[1]</code>)</li>
    </ol>




</dd>
    <dt>
    <a name = "column"></a>
    <strong>column (a, j)</strong>
    </dt>
    <dd>
    extract a column from the 2D array.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
        <li><span class="parameter">j</span>
         column index
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        1d array
    </ol>




</dd>
    <dt>
    <a name = "row"></a>
    <strong>row (a, i)</strong>
    </dt>
    <dd>
    extract a row from the 2D array.
 Added in line with <a href="../libraries/pl.array2d.html#column">column</a>, for read-only purposes directly
 accessing a[i] is more performant.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
        <li><span class="parameter">i</span>
         row index
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        1d array (copy of the row)
    </ol>




</dd>
    <dt>
    <a name = "map"></a>
    <strong>map (f, a, arg)</strong>
    </dt>
    <dd>
    map a function over a 2D array


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">f</span>
            <span class="types"><span class="type">func</span></span>
         a function of at least one argument
        </li>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
        <li><span class="parameter">arg</span>
         an optional extra argument to be passed to the function.
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        2d array
    </ol>




</dd>
    <dt>
    <a name = "reduce_rows"></a>
    <strong>reduce_rows (f, a)</strong>
    </dt>
    <dd>
    reduce the rows using a function.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">f</span>
            <span class="types"><span class="type">func</span></span>
         a binary function
        </li>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        1d array
    </ol>


    <h3>See also:</h3>
    <ul>
         <a href="../libraries/pl.tablex.html#reduce">pl.tablex.reduce</a>
    </ul>


</dd>
    <dt>
    <a name = "reduce_cols"></a>
    <strong>reduce_cols (f, a)</strong>
    </dt>
    <dd>
    reduce the columns using a function.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">f</span>
            <span class="types"><span class="type">func</span></span>
         a binary function
        </li>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        1d array
    </ol>


    <h3>See also:</h3>
    <ul>
         <a href="../libraries/pl.tablex.html#reduce">pl.tablex.reduce</a>
    </ul>


</dd>
    <dt>
    <a name = "reduce2"></a>
    <strong>reduce2 (opc, opr, a)</strong>
    </dt>
    <dd>
    reduce a 2D array into a scalar, using two operations.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">opc</span>
            <span class="types"><span class="type">func</span></span>
         operation to reduce the final result
        </li>
        <li><span class="parameter">opr</span>
            <span class="types"><span class="type">func</span></span>
         operation to reduce the rows
        </li>
        <li><span class="parameter">a</span>
         2D array
        </li>
    </ul>





</dd>
    <dt>
    <a name = "map2"></a>
    <strong>map2 (f, ad, bd, a, b, arg)</strong>
    </dt>
    <dd>
    map a function over two arrays.
 They can be both or either 2D arrays


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">f</span>
            <span class="types"><span class="type">func</span></span>
         function of at least two arguments
        </li>
        <li><span class="parameter">ad</span>
            <span class="types"><span class="type">int</span></span>
         order of first array (<code>1</code> if <code>a</code> is a list/array, <code>2</code> if it is a 2d array)
        </li>
        <li><span class="parameter">bd</span>
            <span class="types"><span class="type">int</span></span>
         order of second array (<code>1</code> if <code>b</code> is a list/array, <code>2</code> if it is a 2d array)
        </li>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">tab</span></span>
         1d or 2d array
        </li>
        <li><span class="parameter">b</span>
            <span class="types"><span class="type">tab</span></span>
         1d or 2d array
        </li>
        <li><span class="parameter">arg</span>
         optional extra argument to pass to function
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        2D array, unless both arrays are 1D
    </ol>




</dd>
    <dt>
    <a name = "product"></a>
    <strong>product (f, t1, t2)</strong>
    </dt>
    <dd>
    cartesian product of two 1d arrays.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">f</span>
            <span class="types"><span class="type">func</span></span>
         a function of 2 arguments
        </li>
        <li><span class="parameter">t1</span>
            <span class="types"><span class="type">array</span></span>
         a 1d table
        </li>
        <li><span class="parameter">t2</span>
            <span class="types"><span class="type">array</span></span>
         a 1d table
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        2d table
    </ol>



    <h3>Usage:</h3>
    <ul>
        <pre class="example">product(<span class="string">'..'</span>,{<span class="number">1</span>,<span class="number">2</span>},{<span class="string">'a'</span>,<span class="string">'b'</span>}) == {{<span class="string">'1a'</span>,<span class="string">'2a'</span>},{<span class="string">'1b'</span>,<span class="string">'2b'</span>}}</pre>
    </ul>

</dd>
    <dt>
    <a name = "flatten"></a>
    <strong>flatten (t)</strong>
    </dt>
    <dd>
    flatten a 2D array.
 (this goes over columns first.)


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         2d table
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        a 1d table
    </ol>



    <h3>Usage:</h3>
    <ul>
        <pre class="example">flatten {{<span class="number">1</span>,<span class="number">2</span>},{<span class="number">3</span>,<span class="number">4</span>},{<span class="number">5</span>,<span class="number">6</span>}} == {<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>,<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>}</pre>
    </ul>

</dd>
    <dt>
    <a name = "reshape"></a>
    <strong>reshape (t, nrows, co)</strong>
    </dt>
    <dd>
    reshape a 2D array.  Reshape the aray by specifying a new nr of rows.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
        <li><span class="parameter">nrows</span>
            <span class="types"><span class="type">int</span></span>
         new number of rows
        </li>
        <li><span class="parameter">co</span>
            <span class="types"><span class="type">bool</span></span>
         use column-order (Fortran-style) (default false)
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        a new 2d array
    </ol>




</dd>
    <dt>
    <a name = "transpose"></a>
    <strong>transpose (t)</strong>
    </dt>
    <dd>
    transpose a 2D array.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        a new 2d array
    </ol>




</dd>
    <dt>
    <a name = "swap_rows"></a>
    <strong>swap_rows (t, i1, i2)</strong>
    </dt>
    <dd>
    swap two rows of an array.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2d array
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         a row index
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         a row index
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        t (same, modified 2d array)
    </ol>




</dd>
    <dt>
    <a name = "swap_cols"></a>
    <strong>swap_cols (t, j1, j2)</strong>
    </dt>
    <dd>
    swap two columns of an array.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2d array
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         a column index
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         a column index
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        t (same, modified 2d array)
    </ol>




</dd>
    <dt>
    <a name = "extract_rows"></a>
    <strong>extract_rows (t, ridx)</strong>
    </dt>
    <dd>
    extract the specified rows.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
        <li><span class="parameter">ridx</span>
            <span class="types"><span class="type">{int}</span></span>
         a table of row indices
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        a new 2d array with the extracted rows
    </ol>




</dd>
    <dt>
    <a name = "extract_cols"></a>
    <strong>extract_cols (t, cidx)</strong>
    </dt>
    <dd>
    extract the specified columns.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         2d array
        </li>
        <li><span class="parameter">cidx</span>
            <span class="types"><span class="type">{int}</span></span>
         a table of column indices
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        a new 2d array with the extracted colums
    </ol>




</dd>
    <dt>
    <a name = "remove_row"></a>
    <strong>remove_row (t, i)</strong>
    </dt>
    <dd>
    remove a row from an array.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2d array
        </li>
        <li><span class="parameter">i</span>
            <span class="types"><span class="type">int</span></span>
         a row index
        </li>
    </ul>





</dd>
    <dt>
    <a name = "remove_col"></a>
    <strong>remove_col (t, j)</strong>
    </dt>
    <dd>
    remove a column from an array.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2d array
        </li>
        <li><span class="parameter">j</span>
            <span class="types"><span class="type">int</span></span>
         a column index
        </li>
    </ul>





</dd>
    <dt>
    <a name = "parse_range"></a>
    <strong>parse_range (s)</strong>
    </dt>
    <dd>
    parse a spreadsheet range.
 The range can be specified either as 'A1:B2' or 'R1C1:R2C2';
 a special case is a single element (e.g 'A1' or 'R1C1')


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">s</span>
            <span class="types"><a class="type" href="https://www.lua.org/manual/5.1/manual.html#5.4">string</a></span>
         a range (case insensitive).
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>
        <li>
           <span class="types"><span class="type">int</span></span>
        start row</li>
        <li>
           <span class="types"><span class="type">int</span></span>
        start col</li>
        <li>
           <span class="types"><span class="type">int</span></span>
        end row</li>
        <li>
           <span class="types"><span class="type">int</span></span>
        end col</li>
    </ol>




</dd>
    <dt>
    <a name = "range"></a>
    <strong>range (t, rstr)</strong>
    </dt>
    <dd>
    get a slice of a 2D array using spreadsheet range notation.  @see parse_range


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
        <li><span class="parameter">rstr</span>
            <span class="types"><a class="type" href="https://www.lua.org/manual/5.1/manual.html#5.4">string</a></span>
         range expression
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        a slice
    </ol>


    <h3>See also:</h3>
    <ul>
         <li><a href="../libraries/pl.array2d.html#parse_range">array2d.parse_range</a></li>
         <li><a href="../libraries/pl.array2d.html#slice">array2d.slice</a></li>
    </ul>


</dd>
    <dt>
    <a name = "default_range"></a>
    <strong>default_range (t, i1, j1, i2, j2)</strong>
    </dt>
    <dd>
    normalizes coordinates to valid positive entries and defaults.
 Negative indices will be counted from the end, too low, or too high
 will be limited by the array sizes.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         start row (default 1)
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         start col (default 1)
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         end row   (default N)
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         end col   (default M)
 return i1, j1, i2, j2
        </li>
    </ul>





</dd>
    <dt>
    <a name = "slice"></a>
    <strong>slice (t, i1, j1, i2, j2)</strong>
    </dt>
    <dd>
    get a slice of a 2D array.  Note that if the specified range has
 a 1D result, the rank of the result will be 1.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         start row (default 1)
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         start col (default 1)
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         end row   (default N)
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         end col   (default M)
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        an array, 2D in general but 1D in special cases.
    </ol>




</dd>
    <dt>
    <a name = "set"></a>
    <strong>set (t, value, i1, j1, i2, j2)</strong>
    </dt>
    <dd>
    set a specified range of an array to a value.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
        <li><span class="parameter">value</span>
         the value (may be a function, called as <code>val(i,j)</code>)
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         start row (default 1)
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         start col (default 1)
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         end row   (default N)
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         end col   (default M)
        </li>
    </ul>



    <h3>See also:</h3>
    <ul>
         <a href="../libraries/pl.tablex.html#set">tablex.set</a>
    </ul>


</dd>
    <dt>
    <a name = "write"></a>
    <strong>write (t, f, fmt, i1, j1, i2, j2)</strong>
    </dt>
    <dd>
    write a 2D array to a file.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
        <li><span class="parameter">f</span>
         a file object (default stdout)
        </li>
        <li><span class="parameter">fmt</span>
            <span class="types"><a class="type" href="https://www.lua.org/manual/5.1/manual.html#5.4">string</a></span>
         a format string (default is just to use tostring)
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         start row (default 1)
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         start col (default 1)
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         end row   (default N)
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         end col   (default M)
        </li>
    </ul>





</dd>
    <dt>
    <a name = "forall"></a>
    <strong>forall (t, row_op, end_row_op, i1, j1, i2, j2)</strong>
    </dt>
    <dd>
    perform an operation for all values in a 2D array.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">t</span>
            <span class="types"><span class="type">array</span></span>
         2D array
        </li>
        <li><span class="parameter">row_op</span>
            <span class="types"><span class="type">func</span></span>
         function to call on each value; <code>row_op(row,j)</code>
        </li>
        <li><span class="parameter">end_row_op</span>
            <span class="types"><span class="type">func</span></span>
         function to call at end of each row; <code>end_row_op(i)</code>
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         start row (default 1)
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         start col (default 1)
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         end row   (default N)
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         end col   (default M)
        </li>
    </ul>





</dd>
    <dt>
    <a name = "move"></a>
    <strong>move (dest, di, dj, src, i1, j1, i2, j2)</strong>
    </dt>
    <dd>
    move a block from the destination to the source.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">dest</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
        <li><span class="parameter">di</span>
            <span class="types"><span class="type">int</span></span>
         start row in dest
        </li>
        <li><span class="parameter">dj</span>
            <span class="types"><span class="type">int</span></span>
         start col in dest
        </li>
        <li><span class="parameter">src</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         start row (default 1)
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         start col (default 1)
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         end row   (default N)
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         end col   (default M)
        </li>
    </ul>





</dd>
    <dt>
    <a name = "iter"></a>
    <strong>iter (a, indices, i1, j1, i2, j2)</strong>
    </dt>
    <dd>
    iterate over all elements in a 2D array, with optional indices.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         2D array
        </li>
        <li><span class="parameter">indices</span>
            <span class="types"><span class="type">bool</span></span>
         with indices (default false)
        </li>
        <li><span class="parameter">i1</span>
            <span class="types"><span class="type">int</span></span>
         start row (default 1)
        </li>
        <li><span class="parameter">j1</span>
            <span class="types"><span class="type">int</span></span>
         start col (default 1)
        </li>
        <li><span class="parameter">i2</span>
            <span class="types"><span class="type">int</span></span>
         end row   (default N)
        </li>
        <li><span class="parameter">j2</span>
            <span class="types"><span class="type">int</span></span>
         end col   (default M)
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        either <code>value</code> or <code>i,j,value</code> depending on the value of <code>indices</code>
    </ol>




</dd>
    <dt>
    <a name = "columns"></a>
    <strong>columns (a)</strong>
    </dt>
    <dd>
    iterate over all columns.


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        column, column-index
    </ol>




</dd>
    <dt>
    <a name = "rows"></a>
    <strong>rows (a)</strong>
    </dt>
    <dd>
    iterate over all rows.
 Returns a copy of the row, for read-only purrposes directly iterating
 is more performant; <code>ipairs(a)</code>


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">a</span>
            <span class="types"><span class="type">array</span></span>
         a 2D array
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        row, row-index
    </ol>




</dd>
    <dt>
    <a name = "new"></a>
    <strong>new (rows, cols, val)</strong>
    </dt>
    <dd>
    new array of specified dimensions


    <h3>Parameters:</h3>
    <ul>
        <li><span class="parameter">rows</span>
            <span class="types"><span class="type">int</span></span>
         number of rows
        </li>
        <li><span class="parameter">cols</span>
            <span class="types"><span class="type">int</span></span>
         number of cols
        </li>
        <li><span class="parameter">val</span>
         initial value; if it's a function then use <code>val(i,j)</code>
        </li>
    </ul>

    <h3>Returns:</h3>
    <ol>

        new 2d array
    </ol>




</dd>
</dl>


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